A field emission electron source composed of carbon nanotube (hereinafter, referred to as a carbon nanotube electron source) is known in that it enables higher luminance and more highly stable field emission current to be obtained than those of a known field emission electron source. However, the electron beam pattern from the carbon nanotube electron source, strongly depends on the tip-end shape of the carbon nanotube, and when the tip-end of the carbon nanotube has a closed structure and a symmetrical shape, a symmetrical and homogeneous beam pattern, as disclosed in Hata. K.: Surf. Sci. 490, pp 296-300 (2001) (non patent document 1), is obtained, since there is no technology for controlling the tip-end shape of the carbon nanotube, even if the tip-end of the carbon nanotube has a closed structure, in many cases it has an asymmetrical shape. In that case, an asymmetrical electron beam pattern as disclosed in M. J. Fransen: Appl. Surf. Sci. 146, pp 312-327 (1999) (non patent document 2), can be obtained. Further, in many cases, a high-luminance beam pattern does not appear at the central portion of an electron beam pattern.